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Family house with offices
Hejna, Vladimír ; Besedová, Klára (referee) ; Čuprová, Danuše (advisor)
This work deals with the single-family detached house including an office. The result is a three-storey partial basement building with built in garage intended for 2 cars. The roof of the house is flat and single casing. The ground plan of the house has rectangular shape, the building is located in the slightly sloping plot in a quiet area of family houses. The main entrance including the plot entrance is oriented to the north. All rooms are naturally litand ventilated. For the skeleton, the building system KM beta is used.
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Detached house with law office
Mikuška, Tomáš ; Tomíček, Oldřich (referee) ; Ostrý, Milan (advisor)
The bachelor thesis solves the design of modern house with a law firm in Povážské Podhradí. This is a three-storey building with a partial basement and with flat single shell roof, which is designed for 3-4 persons to stay and single floor object for law firm. The main construction system is masonry made of wood-cement blocks IZOBLOK.Buildings entrances are situated on the northern side.
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Teaching algebraic expressions using algebra tiles
Kuchaříková, Gabriela ; Vondrová, Naďa (advisor) ; Novotná, Jarmila (referee)
The primary goal of this thesis is to prepare and carry out an education programme on algebraic expressions with variables for eight grade primary school students. This is so they can understand the basic principles of operations with simple algebraic expressions. The secondary goal was to determine whether this education method can also be applied in an online environment, which became a necessity during the Covid-19 pandemic. The theoretical chapter of the thesis covers the introduction of the symbolic language of algebra and the ways of understanding a letter (variable). It contains the definition of basic algebraic terminology in a primary school environment as well as an analysis of select textbooks. Additionally, student work levels with algebraic expressions and a categorization of students' mistakes in operations are used as supplementary grounds for the experimental chapter of the thesis. Finally, the two types of algebra tiles are presented. The experimental chapter of the thesis is aimed at the propaedeutics of algebra tiles via operations with integers, at teaching variable expressions using algebra tiles and at expanding the method of teaching expressions in primary school (Vieta's formulas, completing the square). This chapter's sections cover the respective expression operations and...
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Tiling problems in combinatorics
Dvořáková, Tereza ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
The thesis represents a collection of solved problems concerned with covering planar shapes (mostly rectangles with integer sides) by tiles known as polyominoes (e.g., domi- noes, trominoes, tetrominoes, etc.). In most cases, the goal is to find a tiling or to prove that no such tiling exists. In more difficult problems, the task is to deduce conditions for the rectangle to be tileable by specified polyominoes. The last chapter is devoted to calcu- lating the number of all possible tilings of the specified rectangle.
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Understanding of formulas for areas and volumes of geometric figures in the history of mathematics and in pupils
Tavačová, Adela ; Kvasz, Ladislav (advisor) ; Vondrová, Naďa (referee)
Title: Understanding Area and Volume Formulae of Geometric Figures in the History of Mathematics and by Pupils Author: Bc. Adela Tavačová Supervisor: prof. RNDr. Ladislav Kvasz, DSc. The aim of this thesis is to describe the nature and possible causes of problematic areas in pupils' understanding of area and volume of geometric shapes and solids and treat this issue from the point of view of its ontogeny and phylogeny. Modern theories of gradual formation of the concepts of area and volume in pupils' minds will be characterized, together with the historical development of these concepts (from ancient Egypt and Greece to modern day). Complex analysis of the current Mathematics course books for primary and lower-secondary level is offered in the second part of the thesis. The analysis is based on the criteria following from the study of academic literature and on the historic research in this area. The aim of the analysis is to describe the way in which the course books treat geometric formulae and to what extent they respect their gradual development. In the final discussion, general aspects leading from the analysis will be summarized and offered as possible inspiration for pupils, teachers and future teachers of Mathematics. Key Words: formula, area, volume, algebraic language, hypothetical...
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Packing rectangles
Pavlík, Tomáš ; Šámal, Robert (advisor) ; Mareš, Martin (referee)
This thesis studies the open problem of packing rectangles. Is it possible to pack rectangles with dimensions 1/n x 1/(n+1) into a unit square? The aim of this thesis is analysis of the problem and the related algorithm. Attention will be focused mainly on the implementation of this algorithm and on study of its functioning. Powered by TCPDF (www.tcpdf.org)
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Tiling problems in combinatorics
Dvořáková, Tereza ; Slavík, Antonín (advisor) ; Halas, Zdeněk (referee)
The thesis represents a collection of solved problems concerned with covering planar shapes (mostly rectangles with integer sides) by tiles known as polyominoes (e.g., domi- noes, trominoes, tetrominoes, etc.). In most cases, the goal is to find a tiling or to prove that no such tiling exists. In more difficult problems, the task is to deduce conditions for the rectangle to be tileable by specified polyominoes. The last chapter is devoted to calcu- lating the number of all possible tilings of the specified rectangle.
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Competitive filling of a plane region
Slabý, David ; Valtr, Pavel (advisor) ; Valla, Tomáš (referee)
Two players take alternating turns filling a rectangular board with unit squares without rotation, but may be otherwise arbitrary. Squares may not overlap and the game ends when there is no space for the next one. The result of the game is the number of turns. The constructor aims to maximize this quantity while the destructor wants to minimize it. We would like to get close to this value, provided that both players use their optimal strategy. We prove some new lower and upper bound for the game. This thesis extends results given by Tamás Hubai in his paper Competitive rectangle filling. Furthermore, we have a look at other board shapes and shapes to fill with.
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Detached house with law office
Mikuška, Tomáš ; Tomíček, Oldřich (referee) ; Ostrý, Milan (advisor)
The bachelor thesis solves the design of modern house with a law firm in Povážské Podhradí. This is a three-storey building with a partial basement and with flat single shell roof, which is designed for 3-4 persons to stay and single floor object for law firm. The main construction system is masonry made of wood-cement blocks IZOBLOK.Buildings entrances are situated on the northern side.
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Family house with offices
Hejna, Vladimír ; Besedová, Klára (referee) ; Čuprová, Danuše (advisor)
This work deals with the single-family detached house including an office. The result is a three-storey partial basement building with built in garage intended for 2 cars. The roof of the house is flat and single casing. The ground plan of the house has rectangular shape, the building is located in the slightly sloping plot in a quiet area of family houses. The main entrance including the plot entrance is oriented to the north. All rooms are naturally litand ventilated. For the skeleton, the building system KM beta is used.
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